Electronic squaring circuit



y 1959 H. HARMUTH 2,887,576

ELECTRONIC SQUARING CIRCUIT Filed Nov. 10, 1954 INVENTOR.

HENNING HARMUTH United States Patent O ELECTRONIC SQUARING CIRCUITHenning Harmuth, Red Bank, N.J., assignor to the United States ofAmericaasrepresented by the Secretary of the Army I Application November10, 1954, Serial No. 468,175

2 Claims. (Cl. 250-27) (Granted under Title 35, US. Code (1952), sec.266) The invention described herein may be manufactured and usedby orfor the Government of the United States for governmental purposes,withoutthe payment of any royalty thereon.

The invention relates to a new and useful electronic squaring circuitfor use in analog computers or the like. The circuit operates to derivean algebraic square function of a voltage representative of anotherfunction, and performs this operation without the use of any mechanicallinkage or other moving parts.

Electron tube circuits have been previously used for squaring circuits.The tubes used in such circuits are normally operated on the curvedportion of their static characteristics where the grid voltage-platecurrent curves follow a square law relationship. Such previous circuitshave, however, produced only a rough approximation of the algebraicfunction due to the presence of higher order current components in theoutput circuit. While the magnitude of such higher order components isusually small, the fourth order component particularly, cannot always bedisregarded.

It is the principal object of the present invention to produce anelectronic squaring circuit in which the higher order current componentsare eliminated from the output circuit.

It is a further object of the present invention to devise a method foreliminating'high order components from the output of an electricalsquaring circuit,

It is a further object of the present invention to provide a squaringcircuit wherein the higher order components of suificient magnitude toaffect the result are removed from the output circuit.

It is a still further object of the invention to provide a circuit whichexhibits a quadratic relationship between its input and output circuits.

Other objects and many attendant advantages of the invention will becomemore readily apparent as the same becomes better understood from thefollowing detailed description and the drawing wherein:

The sole figure is a schematic drawing of an electronic squaring circuitconstructed in accordance with the principles of the invention.

The squaring circuit, as shown in the drawing, comprises a phaseinverting input device such as a transformer 11 having a primary winding13 and a centertapped secondary winding 15. Obviously, however, any ofthe conventional phase inverter circuits well known in the prior art maybe used in place of transformer 11. The primary winding 13" is connectedto a pair of input terminals 17 and 19. The center tap of the secondarywinding 15 is connected to ground and the ends thereof are connectedthrough a pair of resistors 21 and 23 to the input circuits'of a pair ofelectron discharge tubes 25 and 27. The electron discharge tubes 25 and27 are illustrated as triodes but need not be of this type. charge tubewhich has a portion of its characteristic which follows a square lawvariation of output to input may be used. Pentodes, for example, willserve equally Any dis- 37 of a source of bias voltage not shown. Thecathodes of tubes 25 and 27 are grounded and the anodes thereof' areconnected in parallel through leads 39, 41, 43 and a plate resistance 42to positive terminal 47 of a source of plate supply not shown. A load orutilization device such as meter 45 is coupled through a condenser 44between the anodes of the tubes and a ground terminal 46 to measure theA.C. component of the voltage on the anodes.

The secondary winding 15 is also connected through a pair of condensers49 and 51 across a second pair of grid leak resistors 53 and 55 and togrids 66 and 68 of a second pair of electron discharge tubes 65 and 67.The junction between the grid leak resistors 53 and 55 is con nected toa terminal 57 which is adapted to be connected to the same negativeterminal of the bias source (not shown) as the terminal 37. The cathodesof discharge. tubes 65 and 67 are connected to ground while the anodesare connected in parallel by leads 69 and 71 and are in turn connectedto the plate supply terminal 47 through the lead 73 and the resistor 42.It will be noted that the anode-cathode circuits of all four electrondischarge devices areconnected in parallel.

The values of the resistors and condensers used in the discharge tubeinput circuits are chosen to bear a predetermined relationship to oneanother. The absolute values used are not critical but the relationshipbetween them should be substantially as set out below,

The value ofthe grid leak resistors 33 and 35 is chosen as a referencebasis. These resistors should be equal and their ohmic resistance may bedesignated as R. The resistance of the resistors 21 and 23 should thenbe approximately equal to R( /21).

The condensers 49 and 51 together with the grid leak resistors 53 and 55constitute phase shift networks. The manner in which the relative valueof their circuit constants is obtained is set out below in thedescription of the circuit operation.

The upper portion of the circuit described above, which includes theelectron discharge tubes 25 and 27, has its grid circuits connected inpush-pull and its anodecathode circuits connected in parallel. Themagnitude of the bias voltage, e is chosen so that the tubes operate onthe curved portion of their characteristics where the grid voltage andplate current maintain a square law relationship.

,Under these conditions of operation, i and i the plate currents throughthe tubes 25 and 27 respectively, may be shown to be power series of theform:

where i =the current through tube 25, i =the current through tube 27, e=the input voltage and a a a a and 51 are constants.

It will be noted that the tubes 25 and 27 are connected so that theircurrents add in the meter 45 so that the two expressions of platecurrent set out above must be added to obtain the total plate currentthrough tubes 25 and 27.

Adding Equations land 2, the terms containing odd powers of the signalinput voltage cancel out with the result that the total currentexpression is:

Since the odd terms have been eliminated, the current through tubes 25and 27 thus 'bears a non-linear relationship to the signal input voltageand the total current is one containing even power components only.

Since a squaring circuit is desired the even powers above the secondmust be eliminated from the current expression, or at least as many ofthem as may be significant in magnitude. This is accomplished by theoperation of the discharge tubes'65 and 67 together with their inputnetworks which include condensers 49 and 51 and the grid resistors 53and 55.

f The condenser 49 and the resistor 55 constitute a phase shift networkand to eliminate the fourth order component of current their values arechosen to satisfy the relationship:

where:

R the resistance of the resistor 55 in ohms, w=21r the frequency of e,,and C=the capacitance of the condenser in farads.

' It will be apparent therefore, that this network causes a phase shiftof 45 and that the voltage applied to the grid 68 of tube 67 may bewritten in complex notation as:

The values of condenser 51 and resistor 53 are equal to those ofcondenser 49 and resistor 55 and satisfy the same relationship. Thevoltage on the grid 66 of tube 65 may be Written as:

: Tubes 65 and 67, being connected in the same manner as tubes 25 and27, their respective platecurrents will he of the form:

Reducing the complex quantities of Equations 4 and 5 and adding them thesum of the plate currents of tubes 65 and 67 is:

Now adding Equations 3 and 6 to obtain the total plate current of allthe tubes:

7 are those of the sixth order and above.

current component of the voltage drop across resistor 42.

The value read on meter 45 will therefore be:

where It will be noted that the 2a term of Equation 7 which is theconstant or direct current component disappears from the final resultdue to the condenser coupling.

The remaining higher order even terms in the power expansion which arenot cancelled from the output current These terms may, if desired, beremoved from the output current by an extension of the same principlethough their magnitude is usually so small that for most practicalpurposes they may be neglected. If it is desired to remove the sixthorder terms a further pair of square law biased electron discharge tubesis necessary. These additional tubes would be connected with their platecircuits in parallel with the tubes 25, 27, 65 and 67, and would havetheir grids energized from the secondary winding 15 through phaseshifting networks that would proto the sum of the above currents throughthe tubes. The

meter 45 is coupled to the anodes of the tubes through condenser 44 andhence measures ,only the' alternating 1r Z radians or where n is thelowest order component to be removed by the particular pair of tubes.

The particular location of the phase shifting circuits for the gridcircuits of the tube is, of course, not critical. It will be obvious,for example, that the phase shift circuit could be connected to inputterminals 17 and 19 and the output thereof connected to a phasesplitting or shifting transformer which, in turn,.would be connected tothe grid circuit of the tubes 65 and 67.

It will be apparent that the above described squaring circuit,constructed in accordance with the principles of the invention,emphasizes the second order or square component of the input functionwhile eliminating the other components which may cause a significanterror in the output.

While there has been disclosed What is considered at present to be thepreferred embodiment of the invention, it will be obvious to thoseskilled in the art that various changes and modifications may be madetherein without departing from the invention, and it is therefore theaim of the appended claims to cover all such changes and modificationsas fall within the true spirit and scope of the invention.

What is claimed is:

1. An analogue electronic squaring circuit comprising a first means forproducing a first voltage proportional to a value to be squared, asecond means for producing a second voltage proportional to the value tobe squared, means connected to the first and second means for producingtwo voltages each dilfering from the square of the first and secondvoltages by the inclusion of a fourth order voltage component ofsubstantial magnitude, means connected to the second means for shiftingthe phase of the second voltage through forty-five degrees whereby thefourth order voltage components will be one hundred and eighty degreesout of phase, means for combining the squared voltages whereby saidfourth order voltage components will cancel, and means for indicatingthe combined voltages.

2. In an analogue electronic squaring circuit comprising a first meansfor producing a first voltage, a second means connected thereto forproducing a voltage in its output differing from the square of the firstvoltage by the inclusion of a fourth order voltage component ofsignificant magnitude, the improvement which comprises a third meansproducing a second voltage equal in magnitude to the first voltage,fourth means connected to said third means for producing a voltage inits output diifering from the square of the second voltage by theinclusion of a fourth order voltage component of the same significantmagnitude, means for shifting the phase of the second voltage relativeto the first voltage through an angle equal to forty-five degreeswhereby the fourth order voltage components in the outputs of saidsecond and fourth means will be in phase opposition, means for combiningthe outputs of said second and fourth means and means connected to saidlast named means for indicating the combined voltage thereof.

References Cited in the file of this patent UNITED STATES PATENTS

